Minorize–maximize algorithm for the generalized odds rate model for clustered current status data

Abstract

Current status data are widely used in epidemiology and public health, where the only observable information is the random inspection time and the event status at inspection. This article presents a unified methodology to analyze such complex data subject to clustering. Given the random clustering effect, the time to event is assumed to follow a semiparametric generalized odds rate (GOR) model. The nonparametric component of the GOR model is approximated via penalized splines, with a set of knot points that increase with the sample size. The within-subject correlation is accounted for by a random (frailty) effect. For estimation, a novel MM algorithm is developed that allows the separation of the parametric and nonparametric components of the model. This separation makes the problem conducive to applying the Newton–Raphson algorithm that quickly returns the roots. The work is accompanied by a complexity analysis of the algorithm, a rigorous asymptotic proof, and the related semiparametric efficiency of the proposed methodology. The finite sample performance of the proposed method is assessed via simulation studies. Furthermore, the proposed methodology is illustrated via real data analysis on periodontal disease studies accompanied by diagnostic checks to identify influential observations.